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1
Morphological Attribute Profiles for the Analysis
of Very High Resolution Images
Mauro Dalla Mura, Student Member, IEEE, Jón Atli Benediktsson, Fellow, IEEE,
Björn Waske, Member, IEEE, and Lorenzo Bruzzone, Fellow, IEEE
Abstract—Morphological attribute profiles (APs) are defined as
a generalization of the recently proposed morphological profiles
(MPs). APs provide a multilevel characterization of an image
created by the sequential application of morphological attribute
filters that can be used to model different kinds of the structural
information. According to the type of the attributes considered in
the morphological attribute transformation, different parametric
features can be modeled. The generation of APs, thanks to an
efficient implementation, strongly reduces the computational load
required for the computation of conventional MPs. Moreover, the
characterization of the image with different attributes leads to a
more complete description of the scene and to a more accurate
modeling of the spatial information than with the use of conventional morphological filters based on a predefined structuring
element. Here, the features extracted by the proposed operators were used for the classification of two very high resolution
panchromatic images acquired by Quickbird on the city of Trento,
Italy. The experimental analysis proved the usefulness of APs
in modeling the spatial information present in the images. The
classification maps obtained by considering different APs result
in a better description of the scene (both in terms of thematic and
geometric accuracy) than those obtained with an MP.
Index Terms—Classification, mathematical morphology, morphological attribute profiles (APs), morphological profiles (MPs),
object detection, remote sensing, very high resolution (VHR)
images.
I. I NTRODUCTION
H
IGH spatial resolution in the latest generation of
optical sensors such as Ikonos, QuickBird, Spot-5, and
Worldview (up to 0.5 m) has increased the range of applications
where remote sensing (RS) data can be usefully employed. The
great amount of thematic information contained in very high
resolution (VHR) images can be exploited in tasks addressing
the analysis of land cover/use and object extraction. In particular, VHR imagery is very useful for investigating urban environments (e.g., in urban growth planning and monitoring, road
Manuscript received October 3, 2009; revised December 3, 2009.
M. Dalla Mura is with the Department of Information Engineering and
Computer Science, University of Trento, 38123 Trento, Italy and also with
the Faculty of Electrical and Computer Engineering, University of Iceland,
101 Reykjavik, Iceland (e-mail: [email protected]).
J. A. Benediktsson is with the Faculty of Electrical and Computer Engineering, University of Iceland, 101 Reykjavik, Iceland (e-mail: [email protected]).
B. Waske is with the Institute of Geodesy and Geoinformation, Department of Photogrammetry, University of Bonn, 53115 Bonn, Germany (e-mail:
[email protected]).
L. Bruzzone is with the Department of Information Engineering and
Computer Science, University of Trento, 38123 Povo, Italy (e-mail: lorenzo.
[email protected]).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TGRS.2010.2048116
network map-updating, discovering building abuse, etc.) where
a detailed representation of the scene can significantly improve
the results of the analysis with respect to low-resolution data
(like those acquired by Landsat Thematic Mapper and Enhanced Thematic Mapper Plus). For example, fine representation of details in a scene can be exploited in object detection
tasks, where the characterization of the geometrical features of
objects is of fundamental importance.
The technical features of VHR data require the development
of specific methods for data analysis. For example, the contextual spectral similarity of connected pixels is a fundamental
property of VHR data, whereas, it is less relevant in mediumresolution images. Furthermore, the fine representation of
geospatial objects and the great amount of details improve the
representation of the surveyed scene but, at the same time,
significantly increase the complexity of VHR images, leading
to a substantial difficulty in extracting the relevant informative
components according to automatic analysis procedures. The
great heterogeneity of the imaged scene (e.g., the same thematic
objects might appear either as homogeneous or highly textured
regions in the image), due to the high resolution of the sensor,
cannot be handled by general image processing techniques
developed for medium/high-resolution sensors. Moreover, the
increased geometrical resolution leads on the one hand to a
fine representation of the scene, whereas, to the other hand
to a decreased resolution in the spectral domain which further
increases the spectral ambiguity of different land-cover types.
This results in a reduction of the effectiveness of conventional
classification methodologies based on the analysis of spectral
features [1]. Thus, features that can be used effectively to model
the spatial information of the pixels by exploiting contextual
relations must be included in the analysis of VHR data.
Several techniques specifically developed for incorporating
information extracted by modeling the spatial properties in
analysis of VHR images have been presented in the literature.
Usually, information extracted from the spatial characteristics
of the image is combined with the available spectral features in the analysis. The spatial information can be extracted
through the application of filters by performing a contextual
image transformation, i.e., an image mapping that transforms
a pixel as a function of the values of a set of pixels (usually
its neighbors). In most cases, the transformation reduces, in
some ways, the complexity of the scene by attenuating some
details. The outcome of the transformation depends on how
the structures that are present in the image interact with the
neighborhood of the filter. Since, particularly in VHR images,
the shapes and contours of the regions are perceptually very
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significant, the filtering technique should simultaneously attenuate the unimportant details and preserve the geometrical
characteristics of the other regions. This property is elegantly
achieved by morphological connected filters, such as filters
by reconstruction [2]. For instance, openings and closings by
reconstruction can suppress brighter and darker regions (with
respect to the graylevel of the adjacent regions), respectively,
that are smaller than the moving window used in the transformation [which is called structuring element (SE)]. On the
contrary, the structures that are larger than the SE are completely preserved, leaving their geometry unaffected. The SE,
which specifies the neighborhood considered for each pixel and
the morphological operator, defines the amount of contextual
relations included in the analysis. Pesaresi and Benediktsson
[3] introduced the application of this family of filters to VHR
images. They performed a multiscale analysis by computing an
anti-granulometry and a granulometry, (i.e., a sequence of closings and openings of increasing size), appended in a common
data structure called morphological profile [3]. The derivative
of the morphological profile (DMP), which shows the residues
of two successive filtering operations (i.e., two adjacent levels
in the profile), was exploited for classifying VHR panchromatic
images and for the definition of a novel segmentation technique. The obtained segmentation map, called morphological
characteristic, is generated by associating each pixel to the level
where the maximum of the DMP (evaluated at the given pixel)
occurs. Since their definition, MPs and DMPs have been widely
used for the analysis of remote sensing images. In [4], the MP
generated by standard opening and closing was computed on a
Quickbird panchromatic image acquired on an area hit by the
2003 Bam earthquake. The spatial features extracted by the MP
were used for assessing the damages caused by the earthquake.
Recently, the standard morphological operators of opening,
closing, white, and black top hat, along with opening and closing by reconstruction, were used together with support vector
machines for the classification of a Quickbird panchromatic
image, [5]. An automatic hierarchical segmentation technique
based on the analysis of the DMP was proposed in [6]. The
segmentation process is performed according to a criterion
based on the spectral homogeneity and spatial connectedness
computed on the segments extracted by the DMP at each level.
The DMP was also analyzed in [7], by extracting a fuzzy measure of the characteristic scale and contrast of each structure
in the image. The computed measures were compared with
the possibility distribution predefined for each thematic class,
generating a value of membership degree for each class used for
classification. In [8], feature extraction techniques were applied
to the DMP in order to reduce the dimensionality of the features
considered by a neural network classifier. In [9], the analysis
based on MPs was successfully extended to the processing of
hyperspectral high-resolution images, by computing the MPs
on the principal components of the data [which were called
extended morphological profiles (EMPs)]. Since the EMP do
not fully exploit the spectral information, in [10], they were
considered along with the original hyperspectral data by a
support vector machines for classification.
As can be observed from the aforementioned literature, the
computation of a multiscale processing (e.g., by MPs, DMPs,
IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING
EMPs) has proven to be effective in extracting informative
spatial features from the analyzed images. For example, MPs
computed with a compact SE (e.g., square, disk, etc.) can be
used for modeling the size of the objects in the image (e.g.,
in [10] this information was exploited for discriminating small
buildings from large ones). Recently, the computation of two
MPs was proposed for modeling both the length and the width
of the structures [11]. In greater detail, one MP is built by diskshaped SEs for extracting the smallest size of the structures,
while the other employs linear SEs (which generate directional
profiles [12]) for characterizing the objects maximum size
(along the orientation of the SE). This is useful for defining the
minimal and maximal length but, as all the possible lengths and
orientations cannot be practically investigated, such analysis is
computationally intensive. Nevertheless, as proven in [13], filters by reconstruction are suitable for handling the geometrical
information of the scene. This was observed by applying filters
by reconstruction in order to reduce the image complexity for
change detection on VHR images. In [14], we introduced the
use of morphological attribute filters for VHR remote sensing
images, as an extension of the common morphological filters by
reconstruction based on SEs. These operators are morphological connected filters. Thus, they process the image without distorting or inserting new edges but only by merging existing flat
regions [2]. Attribute filters were employed for modeling the
structural information of the scene for classification and building extraction in [14] and [15], respectively, where they proved
to be suitable for the modeling of structural information in VHR
images. Attribute filters include in their definition, the morphological operators based on geodesic reconstruction [16]. Moreover, they are a flexible tool since they can perform a processing
based on many different types of attributes. In fact, the attributes
can be of any type. For example, they can be purely geometric,
or related to the spectral values of the pixels, or on different
characteristics. Furthermore, in [15], the problem of the tuning
of the parameters of the filter was addressed by proposing an
automatic selection procedure based on a genetic algorithm.
In this paper, we propose to characterize the spatial information of VHR data by using a multilevel, multi-attribute approach
based on morphological attribute filters. In particular, this paper
aims at extending the works in [14] and [15] by presenting a
formal definition of morphological attribute profiles and differential attribute profiles. These are proposed to be an extension
of the morphological profiles and of their derivative concepts,
which are conventionally defined for openings and closings
by reconstruction. Thus, the proposed theoretical framework
permits the definition of a more general set of profiles based
on the morphological attribute operators. The profiles built by
morphological attribute filters permit a more flexible investigation of the scene, leading to a better modeling of the spatial
information. Moreover, thanks to an efficient implementation,
their application becomes computationally less demanding than
conventional profiles built with operators by reconstruction.
The paper is organized in six sections. The next section
recalls and discusses the concept of morphological profiles.
Section III introduces morphological attribute filters theory. In
Section IV, attribute profiles are formally defined. Section V
presents the results of the experimental analysis carried out for
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DALLA MURA et al.: MORPHOLOGICAL ATTRIBUTE PROFILES
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assessing the effectiveness of the proposed operators in modeling the spatial information. Finally, conclusions are drawn in
Section VI.
II. BACKGROUND ON M ORPHOLOGICAL P ROFILES
In this section, we introduce the concepts of morphological
profiles and differential morphological profiles following the
presentation given in [3]. This leads us to investigate how
the profiles are computed in order to point out the related
limitations. In the following, we recall some useful definitions
for the next discussion.
A. Definitions
A binary image F is a mapping of the subset E, of the image
domain Rn or Zn (usually n = 2, i.e., 2-D images) into the
couple {0, 1}. A grayscale image f (with single tone values)
is a mapping from E to R or Z. Here, we follow the arbitrary
convention of assigning capital letters to binary variables and
binary transformations, whereas small caps refer to grayscale
images and mappings.
A connected component X of a binary image (in [17] also
called a grain) is a set of pixels in which each pair of pixels is
connected. Two pixels are connected according to a connectivity rule. The iso-intensity connected components of a grayscale
image are called flat zones. Common connectivity rules are the
four- and eight-connected, where a pixel is said to be adjacent
to four or eight of its neighboring pixels, respectively. The
connectivity can be extended by more general criteria defining
a connectivity class [18].
A criterion T is a mapping of a generic set S to the couple of
Booleans {false, true}.
An image transformation ψ is a mapping from E to E with
ψ(f ) → R or Z in the grayscale case. We recall some properties
of an image transformation ψ:
• Increasingness: ψ(f ) ≤ ψ(g) if f ≤ g ∀f, g ∈ E
• Anti-extensivity: ψ(f ) ≤ f
• Extensivity: ψ(f ) ≥ f
• Idempotence: ψψ = ψ
• Absorption property: ψi ψj = ψi ψj = ψmax(i,j) .
B. Morphological Profiles
i
Let us first consider an opening by reconstruction, γR
(f ),
applied to an image f with an SE of size i. The opening by
Π(f ) =
Δ(f ) =
Πi :
Πi = Πφλ ,
Πi = Πγλ ,
Δi :
reconstruction can be computed as a sequence of an erosion
with the SE followed by a reconstruction by dilation [2]. By
duality, a closing by reconstruction, φiR (f ), is defined as the
dilation of the original image with SE of size i, followed
by a geodesic reconstruction by erosion [2]. The geodesic
reconstruction, either by dilation or by erosion, is an iterative
procedure that is performed until idempotence is reached.
When opening by reconstruction is computed on the image
with an SE of increasing size, we obtain a morphological
opening profile which can be formalized as
λ
(f ), ∀λ ∈ [0, . . . , n] .
ΠγR (f ) = Πγλ : Πγλ = γR
(1)
This leads to perform a multiscale analysis of the image.
According to its definition, the opening profile is a granulometry built by openings by reconstruction, which is defined
in the mathematical morphology framework as a family of
idempotent, anti-extensive and increasing transformations (i.e.,
openings) that fulfill the absorption property [2]. Analogously,
a morphological closing profile is defined as
ΠφR (f ) = Πφλ : Πφλ = φλR (f ), ∀λ ∈ [0, . . . , n] .
(2)
The closing profile is an anti-granulometry generated by
closings by reconstruction.
When the size, λ, of the SE is zero, then γ 0 (f ) = φ0 (f )
holds, corresponding to the original image f .
A morphological profile, generated by geodesic operators, is
simply the concatenation of closing and opening profiles, as
shown in (3) at the bottom of the page. The resulting MP is
a stack of 2n + 1 images (n images from the closing profile,
the original image and n images from the opening profile). By
computing the derivative of a MP, a differential morphological
profile is generated, as shown in (4) at the bottom of the page.
Above the differential opening profile, Δγ , and the differential
closing profile, Δφ , are respectively defined as
ΔγR (f ) = Δγλ : Δγλ = Πγ(λ−1) − Πγλ , ∀λ ∈ [1, n]
ΔφR (f ) = Δφλ : Δφλ = Πφλ − Πφ(λ−1) , ∀λ ∈ [1, n] .
(5)
(6)
As seen from (4), the DMP stores the residuals of the subsequent increasing transformations applied to the image. This
might be more practical with respect to the MPs for analyzing
the output of the multiscale analysis since the most important
components of the profiles are more evident in the DMP.
with λ = (n − i + 1),
with λ = (i − n − 1),
∀i ∈ [1, n]
∀i ∈ [n + 1, 2n + 1]
Δi = Δφλ , with λ = (n − i + 1),
with λ = (i − n),
Δi = Δγλ ,
∀i ∈ [1, n]
∀i ∈ [n + 1, 2n]
(3)
(4)
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C. Limitations of Morphological Profiles
The main limitation of MPs lies in the partial analysis that is
performed with the computation of the profile. In greater detail,
MPs attempt to model the spatial information within the scene
by analyzing the interaction of a set of SEs of fixed shape and
increasing size with the objects in the image. Although this is a
powerful tool for performing an investigation on the scale of the
structures (thanks to the suitability of the SEs for modeling the
size of the objects), it leads only to a partial characterization of
the objects in the scene. In fact, one could aim at a description
of the image based on other features (e.g., shape, texture, etc.)
rather than the size in order to increase the discriminative
power of the analysis. From a theoretical viewpoint, filters
by reconstruction based on SEs could be used to model other
geometrical features, e.g., to represent the information on the
shape of the regions by analyzing a set of MPs generated by
SEs of different shapes. Nonetheless, the generation of profiles
for different shapes would be computationally unfeasible. In
fact, in order to perform an analysis aimed at modeling the
shape characteristic, the range of the possible sizes assumed
by all the components in the image should be investigated by
each profile in order to remove the dependence of the results to
the scale.
Another important limitation is the strong constraint given
by the use of a SE for modeling the concepts of different
characteristics of the spatial information (e.g., size, shape,
homogeneity, etc.). This limitation is particularly evident when
features more complex than the geometrical primitives of size
and shape are required (e.g., shape factor, length of the skeleton
of a region, etc.). Moreover, SEs are intrinsically unsuitable to
describe features related to the gray-level characteristics of the
regions (e.g., spectral homogeneity, contrast, etc.).
A final limitation of MPs is the computational complexity
associated with their generation. The original image has to
be completely processed for each level of the profile, which
requires two complete processing of the image; one performed
by a closing and the other by an opening transformation. Thus,
the complexity increases linearly with the number of levels
included in the profile.
III. M ORPHOLOGICAL ATTRIBUTE F ILTERS
Morphological attribute openings and attribute thinnings
(called attribute filters) are morphological adaptive filters introduced by Breen and Jones [16]. For simplicity, we introduce
these operators for the binary case and later, we extend the
concepts to the grayscale. The discussion will be focused
first on opening and thinning. Then, the results are reported
analogously for closing and thickening.
A. Binary Attribute Operators
Binary attribute openings operate on connected components
of a binary image according to an increasing criterion. The
transformation removes all those connected components for
which the criterion is not satisfied, leaving the others unaffected. In order to introduce their formal definition, the bi-
nary connected opening and binary trivial opening have to be
defined.
Binary connected opening, Γx , transforms a binary image
f given a pixel x, by keeping the connected component that
contains x and removing all the others. Binary trivial opening
ΓT operates on a given connected component X according to an
increasing criterion T applied to the connected component. If
the criterion is satisfied, the connected component is preserved,
otherwise it is removed according to
X, if T (X) = true
ΓT (X) =
(7)
0, if T (X) = f alse.
In general, one or more features of the connected component,
on which the filter is applied, are compared to a given threshold
defined by the rule. If a criterion T is increasing, then, if it is
satisfied for a connected component X, it will be also satisfied
by all the regions that enclose X (i.e., the superset of X).
Formally for X ⊆ Y , T (X) ⊆ T (Y ). Examples of increasing
criteria are the comparison to a reference value (λ) of the
attributes computed on a region such as the area, the volume
(sum of the graylevels of all the pixels belonging to the region),
the size of the bounding box, etc. It is straightforward to prove
that every region enclosing the one on which these criteria are
computed will have attribute values that are greater or equal
than the computed ones.
Binary attribute opening ΓT , given an increasing criterion
T , is defined as a binary trivial opening applied on all the connected components of F . This can be formally represented as
ΓT (F ) =
ΓT [Γx (F )] .
(8)
x∈F
If the criterion evaluated in the transformation is not increasing,
e.g., when the computed attribute is not dependent itself on the
scale of the regions (e.g., shape factor, orientation, homogeneity, etc.), the transformation also becomes not increasing. Even
if the increasingness property is not fulfilled, the filter remains
idempotent and anti-extensive. For this reason, the transformation based on a non-increasing criterion is not an opening,
but a thinning. Then, analogously to the definition of attribute
openings, binary attribute thinning Γ̃T can be defined as
Γ̃T [Γx (F )]
Γ̃T (F ) =
(9)
x∈F
where Γ̃T denotes a trivial thinning.
All the definitions above can be extended to the respective
dual transformations. Binary attribute closing ΦT .1 Thus, defined as the binary union of the connected components that
fulfill the criterion T
ΦT (F ) =
ΦT [Φx (F )] .
(10)
x∈F
This is based on the operators of ΦT and ΦX , respectively,
binary trivial closing and binary connected closing.
1 In
contrast to [16], here Φ denotes a closing transformation.
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Non-increasing attribute T , leads to a binary attribute thickening Φ̃T given by
(11)
Φ̃T (F ) =
Φ̃T [Φx (F )]
As for attribute thinning, other definitions are available according to the selected filtering rule. For an example of the effects
of attribute filtering, the reader can refer to Fig. 2 (synthetic
image) and Fig. 6 (real remote sensing image).
x∈F
C. Max-Tree
with Φ̃T the binary trivial thickening.
B. Grayscale Attribute Operators
Attribute openings and thinnings introduced for the binary
case can be extended to grayscale images employing the threshold decomposition principle [2]. A grayscale image can be
represented by a stack of binary images obtained by thresholding the original image at each of its graylevels. Then, the
binary attribute opening can be applied to each binary image
and the grayscale attribute opening is given by the maximum
graylevel of the results of the filtering for each pixel and can be
mathematically presented as
γ T (f )(x) = max k : x ∈ ΓT [T hk (f )]
(12)
where T hk (f ) is the binary image obtained by thresholding f
at graylevel k (with k ranging on the graylevels of f ).
The extension to grayscale of the binary attribute thinning
is not straightforward and not unique. For example, a possible
definition of a grayscale attribute thinning can be given analogously to (12) as:
(13)
γ̃ T (f )(x) = max k : x ∈ Γ̃T [T hk (f )] .
However, other definitions are possible, according to the filtering rule considered in the analysis. A list of possible filtering rules is presented in Section III-C. If the criterion T is
increasing, the result of the thinning is actually an opening
transformation. In this case, (13) is equal to (12). Although, this
approach does not lead to the fastest implementation of such
operators, it permits a more direct link to the correspondent
binary operators.
Attribute openings are a family of operators that also includes
openings by reconstruction [16]. If we consider a binary image
with a connected component X and the increasing criterion “the
size of the largest square enclosed by X must be greater than
λ,” the result of the attribute opening is the same as applying an
opening by reconstruction with a squared SE of size λ. The extension of this example to the grayscale case is straightforward.
Given this correspondence between the criterion and the SE, we
point out that any opening by reconstruction can be denoted and
performed as attribute opening.
The concepts presented above are straightforwardly extended
to closing/thickening leading to the definition of grayscale
attribute closing, i.e.,
(14)
φT (f )(x) = min k : x ∈ ΦT [T hk (f )]
and grayscale attribute thickening:
φ̃T (f )(x) = min k : x ∈ Φ̃T [T hk (f )] .
(15)
The Max-tree data representation, introduced by
Salembier et al. [19], is of particular interest because it
increases the efficiency of the filtering by splitting the transformation process into three separate phases: 1) tree creation;
2) filtering; and 3) image restitution. These phases are presented
in detail below.
1) Max-tree creation. For simplicity, let us initially consider
a binary image F . It can be represented in a rooted
tree structure with a depth of two. This is composed by
a single root node, which represents the pixels of the
background, and children nodes connected to the root,
where each of them refers to a connected component
(Ci ) in F . The extension of the tree built for the binary
case to the grayscale can be easily explained by the
threshold decomposition of the image. The levels in the
depth of the tree represent the graylevels of the image
and at each level, the number of nodes corresponds to the
number of connected components present in the binary
image obtained by thresholding the current graylevel.
The tree starts to grow from the root. The connected
component of the root is given by thresholding the image
at its lowest graylevel, thus representing the entire image
domain, E. By increasing the value of the graylevel,
the thresholded image will show separated connected
components, represented by nodes at the level in the tree
corresponding to the threshold. Those nodes are then
linked to their parent nodes at the closest inferior level
in the tree. In the image, each parent node corresponds
to a connected component which is a superset of the connected component represented by the children node in the
tree. The procedure is iterated until the threshold reaches
the maximum graylevel of the image, which defines the
leaves of the tree (the absolute maxima of the image).
2) Filtering. Once the tree is defined, the criterion associated
with the transformation is evaluated at each node (i.e.,
the attribute is checked against a reference value λ). Subsequently, the tree is pruned by removing the nodes that
do not satisfy the criterion according to a filtering rule.
There are two typologies of filtering rules: 1) pruning
strategies, which remove or preserve a node together with
its descendants; and 2) nonpruning strategies, where if
a node is removed, its children are linked to the parent of the removed node. Below we briefly discuss a
few strategies. The Min, Max and the Viterbi decision
rules [19] are pruning strategies, while the Direct and
the Subtractive rules [20] are nonpruning strategies. In
particular, the Subtractive rule proved to be particular
useful when associated to attributes for describing the
shapes of objects [21].
• Min: If a node does not satisfy the criterion, then it
is removed together with all its descendants;
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Fig. 1. Example of the Max-tree representation. (a) Input image and (b) Maxtree structure representing the connected components of the image. Each node
reports also the values of three attributes: area (A), moment of inertia (I) and
standard deviation (S).
• Max: A node that does not satisfy the criterion is
suppressed, only if the criterion is not satisfied by
all of its descendants.
• Direct: If a node does not satisfy the criterion, then
it is removed by leaving unaffected all of its descendants that satisfy it.
• Viterbi: The nodes are removed by evaluating the
costs associated with the decision and by taking the
solution with the minimum cost.
• Subtractive: If a node does not satisfy the criterion,
then it is removed and all its descendants are lowered
by its gray level. A formal definition of the grayscale
attribute thinning operator employing this filtering
rule can be found in [21].
Again, if the criterion is increasing (i.e., the transformation is an opening), all the strategies lead to the same
result.
3) Image restitution. The final phase of the transformation
aims at converting back the pruned tree to an image.
This is done by assigning to each pixel the graylevel
correspondent to the highest level of the tree having a
node whose correspondent connected component in the
image encloses the pixel.
In Fig. 1(b), the Max-tree of a sample image of 1000 × 1000
pixels [Fig. 1(a)] is presented. On each connected component of
the image (correspondent to a node in the tree), three attributes
are computed. Fig. 2 shows the Max-tree of the image pruned
according to different criteria and the correspondent filtered
images. The attributes selected are: 1) area (related the size
of the regions); 2) first moment invariant of Hu [22], also
referred as “moment of inertia” (which models the elongation
of the regions); and 3) standard deviation (which measures the
homogeneity of the pixels enclosed by the regions). The first
moment invariant of Hu can be associated to the moment of
inertia in kinematics because it measures the spread of a region
with respect to its center of mass [22]. The moment of inertia
attribute is a measure of the noncompactness of the objects,
since it has small values for compact regions, while rapidly
increases for the elongated ones [23].
The flexibility of the attribute selection makes these filters
appealing with respect to traditional opening and closing by
reconstruction based on SEs, since any attribute that can be
computed on the regions of the image can be selected for the
analysis. As an example, some attributes that can be interesting
for the analysis of remote sensing images are area, volume
(sum of the intensities of the pixels belonging to each region),
length of the diagonal of the box bounding each region, moment of inertia, shape factor, simplicity and complexity of the
regions [19], homogeneity, standard deviation, and entropy of
the grayscale values of the pixels. Other examples of attributes
used by attribute filters can be found in [16] and other regional
descriptors that can be used as attributes can be found in [23].
The separation of the computation of the attributes and the
filtering phase results in another advantage of this filtering
architecture over the application of conventional operators by
reconstruction. In fact, since the value of the attributes is
computed on all the regions before the filtering phase, it is
possible to avoid defining λ, the threshold value checked by
the criterion, for values that are not significant (e.g., out of the
range of the real values of the attributes).
IV. M ORPHOLOGICAL ATTRIBUTE P ROFILES2
In this section, we introduce the concepts of attribute profiles
(APs) and differential attribute profiles (DAPs). These multilevel filters are based on morphological attribute operators
and they are a generalization of the conventional MPs and
DMPs discussed in Section II-B. For simplicity, we first discuss
in detail the case of anti-extensive idempotent operators (i.e.,
openings and thinnings). Then, we extend the obtained results
to the extensive counterpart (i.e., closings and thickenings).
A. Attribute Profiles
The definition of an attribute opening profile is quite straightforward since a sequence of attribute openings with a family
of increasing criteria T = {Tλ : λ = 0, . . . , n}, with T0 = true
∀X ⊆ E, leads to a granulometry. Thus, attribute opening
profiles can be mathematically defined as
Πγ T (f ) = Πγ Tλ : Πγ Tλ = γ Tλ (f ), ∀λ ∈ [0, . . . , n] . (16)
As for an MP, when λ = 0, Πγ T0 (f ) = γ T0 (f ) = f . We point
out that this definition of attribute opening profile includes
also the morphological opening profile by reconstruction, since
openings by reconstruction are a particular set of attribute
openings. By comparing attribute profiles to conventional MPs,
it can be noticed that both perform multiscale analysis of the
image, since the SE/criterion, driven by the increasing scalar
λ, progressively erases from the image larger structures. Moreover, attribute opening profiles provide the same capabilities
in processing the image as for openings by reconstruction, but
adding more flexibility in the definition of the filtering criterion.
For example, if we consider a compact SE (e.g., square-,
2 A MATLAB application that implements the proposed attribute profiles is
available on request.
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Fig. 2. Examples of attribute filtering on the image of Fig. 1(a). The first row reports the obtained filtered images, the second row the correspondent pruned
Max-tree. Criterion: (a) “area > 20 000”; b) “moment of inertia > 0.25” and (c) “standard deviation > 0.”
disk-shaped), the structures are removed from the scene if the
SE does not fit in them. Thus, the image is processed according
to the smallest size of the regions. If we consider instead the
length of the diagonal of the box bounding each region as an
attribute, then, the structures are filtered according to a measure
of their global extension, which is still related to the concept
of scale, but in a different way with respect to considering the
smallest size of the objects. Moreover, if we take into account
the area of the regions, a different measure of the size of
the objects is provided. Thus, by selecting different type of
attributes, even if they are all increasing measures, different
characterizations of the scale of the structures are generated.
If we consider other types of attributes not constrained by the
increasingness property, a different behavior is achieved by the
filters. For instance, it is possible to assess how the image reacts
to a filtering done on multiple levels with an attribute invariant
to changes in scale. This would permit to characterize the image
by extracting information related to the shape of the structures
through a measure which is independent of their size [21]. Thus,
the application of attribute thinning in a multilevel approach
leads to attribute thinning profiles. However, their definition is
not direct as for attribute opening profiles. In fact, since attribute
thinnings are not increasing, the absorption law might not be
satisfied in the profile. This can result in sequential elements of
the profile that are not ordered. For example, regions erased at
a certain level of the profile might appear again in subsequent
levels associated to more relaxed criteria. This is an undesirable
effect particularly if a derivative of the profile needs to be
computed. In order to build a consistent profile on attribute
thinnings, it is necessary that the absorption law is fulfilled by
the filtered images, leading the AP to be a set of cumulative
functions. This can be obtained by constraining the criteria used
in the filtering. The family of non-increasing criteria U = {Uλ :
λ = 0, . . . , n} considered for computing the profile has to be
an ordered set. Moreover, the criteria have to be consistently
either in the form of Uλ = a(X) > τλ or Uλ = a(X) < τλ for
all the connected component X ⊆ E, and τi ≤ τj for i ≤ j,
with a denoting a generic non-increasing attribute computed
on the component X, and τλ being the scalar value taken as
the threshold at the level λ of the profile. If the criteria are
ordered and defined as mentioned above, then the following rule
holds: If a connected set X ⊆ E does not satisfy the criterion
Ui (i.e., Ui (X) = f alse), then also Uj (X) = f alse, with i ≤ j
and Ui , Uj ∈ U . Thus, for binary trivial thinning, it holds
that if Γ̃Ui (X) = ∅ ⇒ Γ̃Uj (X) = ∅ and this leads Γ̃Ui (F ) ⊆
Γ̃Uj (F ) for binary attribute thinning. In the grayscale case, it
becomes γ̃ Ui (f ) ≤ γ̃ Uj (f ). The latter property corresponds to
the absorption law that can be expresses also as γ̃ Ui γ̃ Uj (f ) =
γ̃ Umax(i,j) (f ). Thus, by selecting these criteria, the profile is
behaving like a granulometry.
Consequently, it is possible to define an attribute thinning
profile, based on a set of ordered criteria U = {Uλ : λ =
0, . . . , n}, with U0 = true ∀X ⊆ E as
Πγ̃ U (f ) = Πγ̃ Uλ : Πγ̃ Uλ = γ̃ Uλ (f ), ∀λ ∈ [0, n] .
(17)
Actually Πγ̃ U includes also Πγ T in its definition since the
attribute thinning profile produces the same results as for the
attribute openings if the criteria U fulfill the more restrictive
property of increasingness. By duality, the attribute closing
profile can be defined as
(18)
Πφ̃U (f ) = Πφ̃Uλ : Πφ̃Uλ = φ̃Uλ (f ), ∀λ ∈ [0, n]
and analogously to (3), we can define an attribute profile as
(19), shown at the bottom of the next page. Attribute thinning
profiles permit us to perform a multilevel analysis of the image
based on attributes (represented by ordered criteria) not necessarily related to the scale of the structures of the image. In
fact, the choice of attributes like the shape factor, the spatial
moments, etc., results in an AP that represents a multilevel (not
multiscale) decomposition of the image according only to the
shape of the regions. Furthermore, the attribute can also be a
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Fig. 3. Examples of four differential profiles computed on four samples belonging to different thematic classes (Vegetation, Road, Building, and Shadow) from
a panchromatic Quickbird image of Trento (Italy). The values of the shown profiles are normalized in the range [0,1]. The horizontal axis reports the levels of the
profiles. In the legend, DMP refers to the conventional DMP built by a squared-SE, DAPa , DAPi , DAPs denote the differential attribute profiles built on the area,
moment of inertia, and standard deviation attribute, respectively. The subtractive rule was considered for the non-increasing criteria. (a) Vegetation. (b) Building.
(c) Road. (d) Shadow.
measure which is not related to the geometry of the regions
but to the graylevels of their pixels. For example, the scene can
be simplified by removing structures according to homogeneity
instead of their scale or shape.
As for MPs, the residuals of the progressive filtering can
be important. Thus we can extend (4) by introducing the
differential attribute profile for the set of non-increasing criteria
U as (20), shown at the bottom of the page, where Δφ̃Uλ
and Δγ̃ Uλ represent the differential thickening and thinning
profiles, respectively, whose definition is straightforward and
thus not reported.
Examples of a DMP and three DAPs computed on a panchromatic Quickbird image of the city of Trento (Italy) for four
different thematic classes are presented in Fig. 3. The attributes
selected for the three DAPs are: 1) area; 2) moment of inertia;
and 3) standard deviation. By analyzing the differential profiles,
Πi = Πφ̃Uλ , with λ = (n − i + 1),
Π(f ) = Πi :
Πi = Πγ̃ Uλ , with λ = (i − n − 1),
Δ(f ) =
Δi :
Δi = Δφ̃Uλ , with λ = (n − i + 1),
with λ = (i − n),
Δi = Δγ̃ Uλ ,
∀i ∈ [1, n]
∀i ∈ [n + 1, 2n + 1]
∀i ∈ [1, n]
∀i ∈ [n + 1, 2n]
(19)
(20)
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Fig. 4. Data set 1—(a) Panchromatic image of 400 × 400 pixels, (b) map of the test areas, and (c) map of the objects selected for the assessment of the
geometrical accuracy.
as expected, it can be noticed that the DMP shows a similar
behavior to the DAP with the area attribute, since both process
shows the image according to the scale of the objects. The
DAPs built on the moment of inertia and the standard deviation
have a different behavior from the scale attributes. However,
given a region, regardless of the type of attribute considered,
the active responses of the pixels belonging to the region in
the profile are all located either in the opening or closing part
of the profile. In fact, dark objects are detected in the closing
profile and bright ones on the opening side. The diversity
shown by considering the DAPs built on different types of
attributes results in features that potentially can increase in the
separability of the information classes.
B. Analysis of the Complexity
The main advantage, in terms of computational complexity,
of the approach based on the Max-tree, with respect to the use of
operators by reconstruction for performing multilevel filtering,
relies on the fact that the image has not to be completely
processed at each level of the profile. In fact, the tree structure
is built only once from the original image and after the attribute
is computed on the components of the image, the same data
structure is pruned by a set of thresholds λ, generating the
filtered images at the different levels. Moreover, we point
out that, if an attribute can be computed incrementally (e.g.,
area, volume, standard deviation, etc.), the computation of the
attribute can be embedded in the creation of the tree, thus
avoiding visiting all the nodes further. If a multilevel, multiattribute analysis is performed, the processing can further take
advantage from the architecture based on the Max-tree. In fact,
the tree is still created only once, and the investigated attributes
can be computed on the nodes, if possible, directly during the
creation of the tree. However, even if the attributes need to be
computed off-line after the creation of the tree, they can be
calculated simultaneously at the visiting of each node, requiring
a single scan of the tree. Moreover, during the computation of
the attributes, their dependences can be exploited. For example,
if the standard deviation and the area attributes need to be
computed, the former requires in its definition the computation
of the area, which can be directly exploited from the second
attribute. Obviously, this further optimizes the analysis. Finally,
the evaluation stage simply checks the criteria against the
attributes values of the nodes in the tree. This is the only
operation in the entire analysis that linearly depends on the
number of levels and attributes considered.
If we quantitatively analyze the computational complexity
of the implementation of the different operators, the conventional opening by reconstruction based on the iterative geodesic
reconstruction [2] has a worst case time complexity with an
upper bound of O(N 2 ), where N is the number of pixels in
the image. When computing a granulometry by reconstruction
composed by L levels, the computational complexity has an
order of 2LN 2 in the worst case. Vincent [24] proposed an
efficient algorithm based on first-input-first-output queue and
two raster scans of the image which is an order of magnitude
faster than the conventional technique and, thus, can reduce
the load of computing a profile. Nevertheless, the image has
to be entirely processed 2L times, regardless the algorithm
considered. Instead, when considering an approach based on
the Max-tree, the computational complexity of the analysis
can be reduced. The most demanding stage of an attribute
filtering based on the Max-tree is the creation of the tree that
relies on a flood-filling algorithm. This algorithm is linear with
respect to both the number of pixels and the connectivity [25].
The pruning of the tree and the image restitution are both
O(N ) operations. Thus, the computational cost of a profile
is O(N G + 4LN ), being G the number of graylevels in the
image. On parallel machines, the Max-tree computation is further speeded up according to a slightly varying implementation
based on the union-find algorithm [26]. More considerations on
the memory use of Max-trees according to their implementation
can be found in [25] and [26].
V. E XPERIMENTAL A NALYSIS
A. Data Set Description
The experimental analysis was carried out by classifying
two portions taken from a large VHR panchromatic image
acquired by the Quickbird sensor on July 2006 with geometric
resolution of 0.6 m. We did not consider the multispectral
images acquired by the Quickbird scanner in order to focus the
analysis only on the capabilities of different APs to model the
geometrical/spatial information. This choice is also reasonable
for some operational conditions when satellites that acquire
only the panchromatic band (e.g., WorldView 1) are used.
The two considered images are made up by 400 × 400
[Fig. 4(a)] and 900 × 900 [Fig. 5(a)] pixels, respectively. Both
the images represent two complex urban areas belonging to the
city of Trento, Italy. Most of the surveyed buildings are residential with heterogeneous size and shape. Some large industrial
buildings are also present in the scene. The presence of shadows
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Fig. 5. Data set 2—(a) Panchromatic image of 900 × 900 pixels, (b) map of the test areas, and (c) map of the objects selected for the assessment of the
geometrical accuracy.
TABLE I
N UMBER OF S AMPLES PER C LASS FOR THE T RAINING AND T EST S ET FOR THE T WO DATA S ETS
can be observed particularly in proximities of buildings. All
these factors contribute to the complexity of the considered
scene.
The pixels of the two images were grouped into four informative classes: 1) Road; 2) Building; 3) Shadow; and 4) Vegetation. For both images, a training set, composed by samples
randomly selected from labeled areas not included in the test
sets, was considered and two independent test sets were defined
by photo-interpretation in order to evaluate the performances
of the classification. One test set is devoted to the evaluation
of the thematic accuracy, while the other checks the geometric
precision of the classification map on a set of selected objects in
the scene according to the protocol proposed in [27] and [28].
The geometrical accuracy is evaluated by a set of five indexes
modeling: 1) oversegmentation (OS); 2) undersegmentation
(US); 3) fragmentation (FG); 4) shape factor (SH); and 5) errors
on the objects borders (ED). The index modeling the OS gives a
measure of the overlap between the region which mostly covers
a reference objects in the classification map and the area of
reference objects. The US error computes how much the regions
correspondending to the reference objects are larger than the
reference objects. The FR index refers to a descriptor of how
the areas of the reference objects are fragmented in different
regions in the classification map. Finally, the SH and the ED
measures indicate how the shapes and the edges, respectively,
of the reference objects differ to those of the correspondent
regions in the reference map. All the error indexes range from
zero to one (in the tables, the values are given in percentages),
with zero representing a perfect match and one the greatest
divergence between the reference objects and the correspondent
regions in the classification map. For further information on
the geometric error indexes, the reader can refer to [28]. The
two test sets are reported in Fig. 4(b) and (c) and Fig. 5(b) and
(c) for data set 1 and 2, respectively. The number of samples
selected for training and testing the two data sets are reported in
Table I.
B. Results
For both the images, a 17-D morphological profile was
generated using a squared-SE with size increasing in eight steps
(7, 13, 19, 25, 31, 37, 43, and 49). These values were arbitrarily
chosen and since they range from 4.2 to 29.4 m, they are able
to model the size of the heterogeneous objects in the scene.
Three attribute profiles with the same dimensionality of the
MP were also created following the approach based on the
Max-tree data structure. All the filtering transformations were
performed on the already constructed tree in order to reduce the
computational burden. For all the APs, the considered criterion
was “the attribute must be greater than λ.”
Three different attributes were considered for the construction of the AP: 1) the area; 2) first moment of Hu; and 3) the
standard deviation. The AP with the area attribute describes the
scale of the structures in the scene; it is the only increasing
attribute among the three selected. In order to create the profile
with the area attribute, the following values of λ were selected:
49, 169, 361, 625, 961, 1369, 1849, and 2401. Although, these
values correspond to the square of the SE sizes used for creating
the MP, the multiscale analysis obtained models; the scale of
the objects in the scene with a different criterion with respect
to the MP. The second attribute considered is the moment
of inertia. The original image was filtered by progressively
suppressing from the scene those regions with attribute smaller
than the following increasing thresholds: 0.2, 0.3, 0.4, 0.5, 0.6,
0.7, 0.8, and 0.9. The AP based on the standard deviation
attribute performs a multilevel decomposition of the objects
in the scene that is not related to the geometry of the regions
but models the homogeneity of the graylevels of the pixels in
the regions. The profile was built according to the following
reference values of the standard deviation: 10, 20, 30, 40, 50,
60, 70, and 80. As for the definition of the SE sizes in the
MP, the threshold values of λ were arbitrarily selected in order
to cover the significant range of variation of the attribute for
all the connected components of the image. Different analyses
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Fig. 6. Extracts of differential profiles built on the first data set. (a) DMP created by a SE with a square shape, DAPs with (b) area attribute, (c) moment of inertia
attribute, and (d) standard deviation attribute. For all the profiles the levels one, three, five, and seven are reported from left to right. All the images are stretched
for visual purposes.
were carried out on the data. At first, each AP was considered
separately and then, all the features extracted by the APs were
taken into account simultaneously.
In order to compare the behavior of the different profiles,
we chose to present the derivatives of the constructed profiles
(i.e., DMP and DAPs) because the differences among them are
perceptually more visible than by analyzing the correspondent
morphological/attribute profiles. The DMP [Fig. 6(a)] is visually similar to the DAP built by evaluating the area attribute
[Fig. 6(b)]. Many regions, which are suppressed at a certain
level in the DMP, are present at the same level in the DAP.
However, some other objects are not revealed at the same level
in the two profiles but in adjacent levels. For example, the thin
and elongated region in the middle of the scene that is present
in the second and third image from the left (levels three and
five, respectively) in the DMP, in the DAP results in the third
and fourth (respectively five and seven). These differences in
the two differential profiles are mainly due to the different
modeling of the concept of scale and to the choice done for
the step size of the SEs and of the values of the thresholds
λ, for the area attribute. In particular, the filters based on the
area attribute remove the structures from the image according to
their cardinality, whereas, the operators by reconstruction with
a square SE interact to the smallest size of each region. Thus,
this different behavior is particularly evident when considering
elongated regions.
Different conclusions can be drawn by comparing the DMP
to the DAPs generated by the moment of inertia and the
standard deviation. At first, it is evident that at higher levels
of the profiles (i.e., related to large values of λ), also regions
that are spatially smaller than some others, appeared in previous
levels, are present. This is due to the non-increasingness of the
selected criterion.
In order to quantitatively compare the capabilities of the
proposed profiles in modeling the spatial characteristics of
the scene, we classified the original image using each profile.
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TABLE II
E RRORS O BTAINED BY C LASSIFYING THE PANCHROMATIC I MAGE A LONG W ITH M ORPHOLOGICAL /ATTRIBUTE P ROFILES FOR DATA S ET 1
TABLE III
E RRORS O BTAINED BY C LASSIFYING THE PANCHROMATIC I MAGE A LONG W ITH M ORPHOLOGICAL /ATTRIBUTE P ROFILES FOR DATA S ET 2
TABLE IV
C LASS S PECIFIC P RODUCER ACCURACY (PA) AND U SER ACCURACY (UA) O BTAINED BY C LASSIFYING THE PANCHROMATIC I MAGE A LONG
W ITH M ORPHOLOGICAL /ATTRIBUTE P ROFILES FOR DATA S ET 1. T HE B EST ACCURACIES O BTAINED A RE M ARKED IN B OLD
A random forest technique with 200 trees was used for the
classification [29]. The random forest classifier is formed by an
ensemble of decision tree classifiers. We chose to use this nonparametric classifier because of the high redundancy shown
by the profiles that can be critical for the estimation of the
statistics in classical parametric classifiers. The classification
is achieved by selecting the output of the ensembles of the
tree classifiers according to a majority voting. The features
considered by the classifier were the panchromatic band and
the generated profiles. For the definition of the split on each
node in the random forest, the number of considered variables
was correspondent to the square root of the number of input
features. The aim of this analysis was to investigate how the
accuracy (both thematic and geometric) varies when including
in the analysis the knowledge gathered on the spatial domain
by the profiles. In particular, the results obtained by considering
the panchromatic band and a conventional MP were compared
to those obtained by different APs.
Tables II and III show the thematic error index, in terms
of percentage overall error and the kappa error (computed as
1-kappa coefficient in percentage) on the test set, and the five
geometric error indexes. Furthermore, the accuracies obtained
by each class are shown in Tables IV and V. In particular, the
producer and user accuracy are reported. We recall that the PA
is computed, for each class, as the total number of the patterns
correctly classified divided by the total number of the patterns
belonging to the considered class in the reference map. The PA
measures how many reference patterns are correctly classified
by each class. The UA is obtained by dividing the total number
of correctly classified patterns for each class by the total number
of patterns classified to the same class. The UA indicates how
many samples associated to a class are actually belonging to
that class in the reference. More information on PA and UA can
be found in [30].
By analyzing the thematic accuracies reported in Table II
for the original panchromatic band, one can observe that a
clear increase of the accuracy is obtained by using jointly
the features that model the spatial information. The accuracy
achieved by considering the MP is comparable to the one
obtained by the single APs with moment of inertia and standard
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TABLE V
C LASS S PECIFIC P RODUCER ACCURACY (PA) AND U SER ACCURACY (UA) O BTAINED BY C LASSIFYING THE PANCHROMATIC I MAGE A LONG
W ITH M ORPHOLOGICAL /ATTRIBUTE P ROFILES FOR DATA S ET 2. T HE B EST ACCURACIES O BTAINED A RE M ARKED IN B OLD
Fig. 7. Data set 1. Classification maps obtained by (a) panchromatic image only, (b) MP, (c) AP area, (d) AP inertia, (e) AP std, (f) AP inertia + AP std, and
(g) AP all.
deviation attributes. Instead, the AP constructed on the area
attribute produced the highest overall error and kappa error
among the profiles. This is due to the selected thresholds used
for computing the filtering, which might not properly model
the great variety in the scale of the objects for the considered
scene. The best results, according to the thematic accuracy, are
obtained by the joint use of the AP with moment of inertia
and the AP with standard deviation attribute, which reduced the
overall classification error by about 24% and the kappa error of
32%, with respect to the use of the only original panchromatic
image. The improvement was about 9% in overall error and
14% in kappa error, with respect to the conventional MP. Even
if the global accuracies are in general quite small, making more
complex the visual interpretation of the maps, by evaluating
the geometric indexes, one can see that the classification of
the panchromatic image shows a large oversegmentation error
(thus, a small undersegmentation error) with respect to the maps
obtained by considering the profiles. This behavior is also confirmed by a visual inspection of the classification maps shown
in Fig. 7. In fact, it is possible to observe that the classification
map obtained with the panchromatic image [Fig. 7(a)] is highly
fragmented, whereas, the other maps are more homogeneous.
As best case, when considering the map obtained by the AP
with moment of inertia, a reduction by about 29% and 7% in
the oversegmentation and fragmentation error, respectively, is
achieved. This effect can be noticed in the row of buildings
at the top of the image. Nevertheless, the AP inertia shows a
high US error which can be due to the missed recognition of
the buildings on the bottom of the image and the generation
of broad areas. The lowest US error among the profiles and
the overall lowest ED error are achieved, by considering the
AP with moment of inertia and the AP with standard deviation
attribute together.
Table III shows the error rates on the test set obtained by
analyzing the data set 2. As for the previous data set, the
thematic errors decrease when considering the spatial information provided by the profiles. Also, in this case, the results
obtained by considering a single AP are similar to those generated by the MP (this is also clear from the classification
maps in Fig. 8). In this experiment, the AP built on the area
attribute results in a thematic error only slightly smaller than
the one of the original panchromatic image (about 4% in
both overall and kappa errors). However, as confirmed by the
map, the geometrical errors are similar with those obtained
by considering the other profiles. Again, the highest thematic
accuracy is obtained when considering the APs with moment
of inertia and standard deviation attributes. The thematic errors
are reduced by about 28% in the overall error and 38% in
kappa errors with respect to the original panchromatic image
and by about 12% and 17% (overall and kappa errors) against
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14
IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING
Fig. 8. Data set 2. (a) Panchromatic band; classification maps obtained by (b) MP, (c) AP area, (d) AP inertia, (e) AP std, (f) AP inertia + AP std, and
(g) AP all.
the conventional MP. As for the first data set, better accuracies
are obtained by considering only the AP with moment of inertia
and the AP with standard deviation attribute than considering
together also the AP with area attribute. This can be due to
the increase in the dimensionality of the feature space given
by considering also the AP with area attribute, which makes
the analysis more complex (i.e., Hughes phenomenon), without
providing enough additional independent information than to
the other APs. However, one should observe that the selection
of the threshold values λs affects the capability of the computed
profile in modeling the spatial features of the objects. Thus, an
AP with different threshold values for the area attribute might
provide features which are more discriminant.
In addition, also the geometry of the reference objects is
globally more precisely preserved by the AP with moment
of inertia and AP with standard deviation attribute considered
together in comparison to the other single profiles. In particular,
the oversegmentation error in the map obtained by considering
all the APs decreases of about 34% and 18%, compared to that
of the map generated by the only panchromatic image and by
the MP, respectively. This can be observed as a more uniform
classification of the vegetated areas in the middle of the image
and of some roads. As for data set 1, the AP inertia shows small
US and FG errors but high US error, which can be due to the
presence of large areas associated to the Vegetation class.
By considering Tables IV and V, it is possible to make a
detailed class-by-class analysis by considering the producer
accuracy (PA) and user accuracy (UA) obtained. The two results
for both the data sets are analyzed together in order to observe
trends in the obtained results. Focusing the attention on the
specific thematic classes, we can underline as, with respect to
the other attributes, the AP with moment of inertia performed
well in identifying the roads, in particular for data set 2.
However, for both data sets, the best results were obtained by
considering all the APs. When considering the Building class,
the conventional MP, the AP with standard deviation attribute,
and the AP with all the attributes performed the best and gave
comparable results. For this particular class, good results were
also obtained by the AP with moment of inertia but only in
data set 1. The class Shadow was globally well-classified by all
the profiles and no particular trend in the results was noticed.
Finally, the vegetated areas were extracted well by the AP with
the standard deviation attribute particualrly in data set 1. The
MP and the AP with moment of inertia and the one with all the
attributes also reached similar results.
VI. C ONCLUSION
In this paper, attribute profiles have been introduced for
classification of very high resolution remote sensing images and
differential attribute profiles have been proposed and formally
defined. The motivation of this work relies on the need to improve the flexibility, the capability of modeling different kind of
objects, and the computational load associated with the widely
used conventional morphological profiles and their derivative.
Attribute profiles can be used for extracting information
from the spatial domain by reducing the limitations of the
morphological profiles. This approach allows one to analyze
the original image in a multilevel fashion by the application
of a sequence of morphological attribute operators. These
operators are adaptive morphological connected filters, which
include in their general definition also opening and closing by
reconstruction. Attribute filters are flexible tools that enable
to analyze an image, not only on the basis of the scale of
the structures (as for operators by reconstruction), but also
according to other measures/attributes computed on the regions.
Thus, it is possible to perform a multilevel analysis of the scene
by exploiting measures related to many different geometric
primitives (e.g., shape), the graylevel of the pixels, or any other
parameter that can be computed on the regions.
In the paper, we propose to compute the attribute profiles according to an effective implementation based on the Max-tree,
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DALLA MURA et al.: MORPHOLOGICAL ATTRIBUTE PROFILES
i.e., an efficient representation of the data, which leads to a
reduction of the computational load of about one order of
magnitude with respect to morphological profiles.
The proposed technique was applied to two very high resolution panchromatic images acquired by Quickbird satellite
on the city of Trento, Italy. Three attribute profiles, based on
different attributes, were extracted from the panchromatic band.
We considered 1) the area (which is related to the MP created
with a squared SE); 2) the moment of inertia (which is a
descriptor of the geometry of a region invariant to the scale);
and 3) the standard deviation of the graylevels of the pixels
(which measures the homogeneity of the regions). The data
were classified by a random forest classifier. The obtained
maps were evaluated by checking their thematic accuracy and
the geometric precision in representing some reference objects in the scene. The results pointed out the effectiveness of
the proposed APs, which involved a sharply higher thematic
and geometric accuracy with respect to considering the only
panchromatic band. Moreover, the profiles built on different
attributes led to similar results in terms of accuracy, but also
conveyed different and complementary information into the
classification process. In fact, the joint use of the three attribute
profiles in the classification tasks resulted in an decrease of the
classification kappa errors up to 38% and 17% with respect
to the only panchromatic image and to the MP, respectively.
The obtained classification maps are also more precise in the
representation of the geometry of the regions as proven by the
geometrical error indexes.
As future developments, we plan to investigate in depth
the capabilities of APs and DAPs in the analysis of very
high resolution images particularly for applications where the
extraction of the spatial information has a fundamental role,
such as the extraction and characterization of the objects in
the scene. Moreover, it would be very interesting to analyze
how the modeling of many different geometrical features can
improve the analysis of multitemporal image series (e.g., for
change detection task) particularly for urban areas.
ACKNOWLEDGMENT
This work was supported in part by the Research Fund of the
University of Iceland and of the University of Trento.
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16
Mauro Dalla Mura (S’08) received the B.S.
(Laurea) and M.S. (Laurea Specialistica) degrees in
telecommunication engineering from the University
of Trento, Trento, Italy, in 2005 and 2007, respectively. He is currently working toward the Ph.D.
jointly between the University of Trento and the
University of Iceland, Reykjavik, Iceland.
Since 2007, he has been with the Remote Sensing
Group at the Department of Information Engineering
and Computer Science, University of Trento and
with the Faculty of Electrical and Computer Engineering, University of Iceland, Reykjavik, Iceland. His main research activities
are in the fields of remote sensing, image processing, and pattern recognition.
In particular, his interests include mathematical morphology, classification, and
change detection.
Mr. Dalla Mura is a Reviewer for the IEEE T RANSACTIONS ON G EO SCIENCE AND R EMOTE S ENSING and the Canadian Journal of Remote
Sensing.
Jón Atli Benediktsson (S’84–M’90–SM’99–F’04)
received the Cand.Sci. degree in electrical engineering from the University of Iceland, Reykjavik,
Iceland, in 1984, and the M.S.E.E. and Ph.D. degrees
from Purdue University, West Lafayette, IN, in 1987
and 1990, respectively.
He is currently Pro Rector for academic affairs and
a Professor of electrical and computer engineering
with the University of Iceland. He has held visiting
positions with the Department of Information and
Communication Technology, University of Trento,
Trento, Italy, since 2002; the School of Computing and Information Systems,
Kingston University, Kingston upon Thames, U.K., during 1999 to 2004; the
Joint Research Centre of the European Commission, Ispra, Italy, in 1998;
the Technical University of Denmark, Lyngby, Denmark, in 1998; and the
School of Electrical and Computer Engineering, Purdue University, in 1995.
In August 1997, he was a Fellow with the Australian Defence Force Academy,
Canberra, A.C.T., Australia. From 1999 to 2004, he was the Chairman of the
energy company Metan Ltd. He was also the Chairman of the University of
Iceland’s Science and Research Committee from 1999 to 2005. Since 2006,
he has been the Chairman of the University of Iceland’s Quality Assurance
Committee. He coedited (with Prof. D. A. Landgrebe) a Special Issue on
Data Fusion of the IEEE T RANSACTIONS ON G EOSCIENCE AND R EMOTE
S ENSING (TGRS) (May 1999) and (with P. Gamba and G. G. Wilkinson)
a Special Issue on Urban Remote Sensing from Satellite (October 2003).
His research interests include remote sensing, pattern recognition, machine
learning, image processing, biomedical engineering, and signal processing, and
he has published extensively in those fields.
Dr. Benediktsson is a member of Societas Scinetiarum Islandica and Tau
Beta Pi. He was the Past Editor and is currently Associate Editor for TGRS
and Associate Editor for the IEEE G EOSCIENCE AND R EMOTE S ENSING
L ETTERS. From 1999 to 2002, prior to being Editor, he was Associate Editor
for TGRS. From 1996 to 1999, he was the Chairman of the IEEE Geoscience
and Remote Sensing Society (GRSS) Technical Committee on Data Fusion and
was elected to the Administrative Committee of the GRSS for the terms 2000 to
2002 and 2008 to 2010. He is currently, the Executive Vice President of GRSS.
In 2002, he was appointed as Vice President of Technical Activities of GRSS,
and in 2008, he was appointed as Vice President of Professional Activities of
GRSS. He was the founding Chairman of the IEEE Iceland Section and served
as its Chairman from 2000 to 2003. He was a member of a NATO Advisory
Panel of the Physical and Engineering Science and Technology Subprogram
(2002–2003). He was a member of Iceland’s Science and Technology Council
(2003–2006) and a member of the Nordic Research Policy Council (2004). He
received the Stevan J. Kristof Award from Purdue University, in 1991, as an
outstanding graduate student in remote sensing. In 1997, he was the recipient
of the Icelandic Research Council’s Outstanding Young Researcher Award. In
2000, he was granted the IEEE Third Millennium Medal. In 2004, he was a
corecipient of the University of Iceland’s Technology Innovation Award. In
2006, he received the yearly research award from the Engineering Research
Institute, University of Iceland. In 2007, he received the Outstanding Service
Award from the IEEE GRSS.
IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING
Björn Waske (S’06–M’08) received the M.Sc. degree in applied environmental sciences with a major
in remote sensing from the University of Trier, Trier,
Germany, in 2002 and the Ph.D. degree from the
University of Bonn, Bonn, Germany, in 2007.
From 2004 to 2007, he was with the Center of
Remote Sensing of Land Surfaces (ZFL), University
of Bonn and visited the Department of Electrical
and Computer Engineering, University of Iceland,
Reykjavik, Iceland for three months in 2006. Until
mid-2004, he was a Research Assistant with the
Department of Geosciences, Munich University, Munich, Germany, where he
worked on the use of remote sensing data for flood forecast modeling. Since
September 2009, he has been an Assistant Professor at the Institute of Geodesy
and Geoinformation, Faculty of Agriculture, University of Bonn. His current
research interests include advanced concepts for image classification and data
fusion, focusing on multisensor applications.
Dr. Waske is a Reviewer for the IEEE T RANSACTIONS ON G EOSCIENCE
AND R EMOTE S ENSING and the IEEE G EOSCIENCE AND R EMOTE S ENSING
L ETTERS.
Lorenzo Bruzzone (S’95–M’98–SM’03–F’10) received the M.S. (Laurea) degree in electronic engineering (summa cum laude) and the Ph.D. degree in
telecommunications from the University of Genoa,
Genoa, Italy, in 1993 and 1998, respectively.
He his currently a Full Professor of telecommunications at the University of Trento, Trento, Italy,
where he teaches remote sensing, pattern recognition, radar, and electrical communications. He is the
Head of the Remote Sensing Laboratory in the Department of Information Engineering and Computer
Science, University of Trento. His current research interests are in the areas
of remote sensing, signal processing, and pattern recognition (analysis of multitemporal images; feature extraction and selection; classification, regression,
and estimation; data fusion; and machine learning). In 2008, was appointed as
a member of the joint NASA/ESA Science Definition Team for Outer Planet
Flagship Missions. He is the author (or coauthor) of 90 scientific publications
in referred international journals (61 in IEEE journals), more than 140 papers
in conference proceedings, and 13 book chapters. He is the Editor/Co-editor
of 10 books/conference proceedings. He is a Referee for many international
journals and has served on the Scientific Committees of several international
conferences. He conducts and supervises research on these topics within the
frameworks of several national and international projects.
Dr. Bruzzone is a member of the Managing Committee of the Italian InterUniversity Consortium on Telecommunications and a member of the Scientific
Committee of the India–Italy Center for Advanced Research. He is also a member of the International Association for Pattern Recognition and of the Italian
Association for Remote Sensing (AIT). Since 2009, he has been a member of
the Administrative Committee of the IEEE Geoscience and Remote Sensing
Society. He was the General Chair and Co-chair of the First and Second IEEE
International Workshop on the Analysis of Multi-temporal Remote-Sensing
Images (MultiTemp), and is currently a member of the Permanent Steering
Committee of this series of workshops. Since 2003, he has been the Chair of the
SPIE Conference on Image and Signal Processing for Remote Sensing. From
2004 to 2006, he served as an Associated Editor of the IEEE G EOSCIENCE
AND R EMOTE S ENSING L ETTERS , and currently is an Associate Editor for
the IEEE T RANSACTIONS ON G EOSCIENCE AND R EMOTE S ENSING (TGRS)
and the Canadian Journal of Remote Sensing. He ranked first place in the
Student Prize Paper Competition of the 1998 IEEE International Geoscience
and Remote Sensing Symposium (Seattle, July 1998). He was a recipient of the
Recognition of IEEE TGRS Best Reviewers in 1999 and was a Guest Co-Editor
of different Special Issues of the IEEE TGRS.
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